当前期刊: Annals of Pure and Applied Logic Go to current issue    加入关注    本刊投稿指南
显示样式:        排序: IF: - GO 导出
我的关注
我的收藏
您暂时未登录!
登录
  • A parametrised functional interpretation of Heyting arithmetic
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2021-01-07
    Bruno Dinis; Paulo Oliva

    This paper presents an abstract parametrised functional interpretation of WE-HAω. It is based on families of parameters allowing for different degrees of freedom on the design of concrete interpretations. In this way, we are able to generalise previous work on unifying functional interpretations by including in the unification the more recent bounded and Herbrandized functional interpretations.

    更新日期:2021-01-13
  • A short note on groups in separably closed valued fields
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2021-01-08
    Silvain Rideau-Kikuchi

    In this note we show that groups with definable generics in a separably closed valued field K of finite imperfection degree can be embedded into groups definable in the algebraic closure of K.

    更新日期:2021-01-13
  • Local collection and end-extensions of models of compositional truth
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2021-01-13
    Mateusz Łełyk; Bartosz Wcisło

    We introduce a principle of local collection for compositional truth predicates and show that it is arithmetically conservative over the classically compositional theory of truth. This axiom states that upon restriction to formulae of any syntactic complexity, the resulting predicate satisfies full collection. In particular, arguments using collection for the truth predicate applied to sentences occurring

    更新日期:2021-01-13
  • Quantum set theory: Transfer Principle and De Morgan's Laws
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2021-01-12
    Masanao Ozawa

    In quantum logic, introduced by Birkhoff and von Neumann, De Morgan's Laws play an important role in the projection-valued truth value assignment of observational propositions in quantum mechanics. Takeuti's quantum set theory extends this assignment to all the set-theoretical statements on the universe of quantum sets. However, Takeuti's quantum set theory has a problem in that De Morgan's Laws do

    更新日期:2021-01-12
  • Long games and σ-projective sets
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2021-01-05
    Juan P. Aguilera; Sandra Müller; Philipp Schlicht

    We prove a number of results on the determinacy of σ-projective sets of reals, i.e., those belonging to the smallest pointclass containing the open sets and closed under complements, countable unions, and projections. We first prove the equivalence between σ-projective determinacy and the determinacy of certain classes of games of variable length <ω2 (Theorem 2.4). We then give an elementary proof

    更新日期:2021-01-12
  • Typical forcings, NP search problems and an extension of a theorem of Riis
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-12-17
    Moritz Müller

    We define typical forcings encompassing many informal forcing arguments in bounded arithmetic and give general conditions for such forcings to produce models of the universal variant of relativized T21. We apply this result to study the relative complexity of total (type 2) NP search problems associated to finitary combinatorial principles. Complexity theory compares such problems with respect to polynomial

    更新日期:2020-12-22
  • The full basis theorem does not imply analytic wellordering
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-12-08
    Vladimir Kanovei; Vassily Lyubetsky

    A finite support product of ω1 clones of Jensen's minimal Π21 singleton forcing is used to define a model in which any non-empty analytically definable set of reals contains an analytically definable real (the full basis theorem), but there is no analytically definable wellordering of the reals.

    更新日期:2020-12-17
  • On the structure of certain valued fields
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-12-09
    Junguk Lee; Wan Lee

    In this article, we study the structure of finitely ramified mixed characteristic valued fields. For any two complete discrete valued fields K1 and K2 of mixed characteristic with perfect residue fields, we show that if the n-th residue rings are isomorphic for each n≥1, then K1 and K2 are isometric and isomorphic. More generally, for n1≥1, there is n2 depending only on the ramification indices of

    更新日期:2020-12-16
  • Continuous extension of maps between sequential cascades
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-12-01
    Szymon Dolecki; Andrzej Starosolski

    The contour of a family of filters along a filter is a set-theoretic lower limit. Topologicity and regularity of convergences can be characterized with the aid of the contour operation. Contour inversion is studied, in particular, for iterated contours of sequential cascades. A related problem of continuous extension of maps between maximal elements of sequential cascades to full subcascades is solved

    更新日期:2020-12-08
  • Sets in Prikry and Magidor generic extensions
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-11-23
    Tom Benhamou; Moti Gitik

    We continue [4] and study sets in generic extensions by the Magidor forcing and by the Prikry forcing with non-normal ultrafilters.

    更新日期:2020-12-01
  • Preserving levels of projective determinacy by tree forcings
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-11-18
    Fabiana Castiblanco; Philipp Schlicht

    We prove that various classical tree forcings—for instance Sacks forcing, Mathias forcing, Laver forcing, Miller forcing and Silver forcing—preserve the statement that every real has a sharp and hence analytic determinacy. We then lift this result via methods of inner model theory to obtain level-by-level preservation of projective determinacy (PD). Assuming PD, we further prove that projective generic

    更新日期:2020-11-27
  • Superstability, noetherian rings and pure-semisimple rings
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-11-05
    Marcos Mazari-Armida

    We uncover a connection between the model-theoretic notion of superstability and that of noetherian rings and pure-semisimple rings. We characterize noetherian rings via superstability of the class of left modules with embeddings. Theorem 0.1 For a ring R the following are equivalent. (1) R is left noetherian. (2) The class of left R-modules with embeddings is superstable. (3) For every λ≥|R|+ℵ0, there

    更新日期:2020-11-12
  • Ramsey transfer to semi-retractions
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-10-21
    Lynn Scow

    We introduce the notion of a semi-retraction. Given two structures A and B, A is a semi-retraction of B if there exist quantifier-free type respecting maps f:B→A and g:A→B such that f∘g is an embedding. We say that a structure has the Ramsey property if its age does. Given two locally finite ordered structures A and B, if A is a semi-retraction of B and B has the Ramsey property, then A also has the

    更新日期:2020-11-09
  • A topological zero-one law and elementary equivalence of finitely generated groups
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-11-04
    D. Osin

    Let G denote the space of finitely generated marked groups. We give equivalent characterizations of closed subspaces S⊆G satisfying the following zero-one law: for any sentence σ in the infinitary logic Lω1,ω, the set of all models of σ in S is either meager or comeager. In particular, we prove that the zero-one law holds for certain natural spaces associated to hyperbolic groups and their generalizations

    更新日期:2020-11-09
  • Lindström theorems in graded model theory
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-11-04
    Guillermo Badia; Carles Noguera

    Stemming from the works of Petr Hájek on mathematical fuzzy logic, graded model theory has been developed by several authors in the last two decades as an extension of classical model theory that studies the semantics of many-valued predicate logics. In this paper we take the first steps towards an abstract formulation of this model theory. We give a general notion of abstract logic based on many-valued

    更新日期:2020-11-09
  • Completion of choice
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-10-28
    Vasco Brattka; Guido Gherardi

    We systematically study the completion of choice problems in the Weihrauch lattice. Choice problems play a pivotal rôle in Weihrauch complexity. For one, they can be used as landmarks that characterize important equivalences classes in the Weihrauch lattice. On the other hand, choice problems also characterize several natural classes of computable problems, such as finite mind change computable problems

    更新日期:2020-11-06
  • More on HOD-supercompactness
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-10-08
    Arthur W. Apter; Shoshana Friedman; Gunter Fuchs

    We explore Woodin's Universality Theorem and consider to what extent large cardinal properties are transferred into HOD (and other inner models). We also separate the concepts of supercompactness, supercompactness in HOD and being HOD-supercompact. For example, we produce a model where a proper class of supercompact cardinals are not HOD-supercompact but are supercompact in HOD. Additionally we introduce

    更新日期:2020-10-16
  • Intuitionistic fixed point logic
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-10-09
    Ulrich Berger; Hideki Tsuiki

    We study the system IFP of intuitionistic fixed point logic, an extension of intuitionistic first-order logic by strictly positive inductive and coinductive definitions. We define a realizability interpretation of IFP and use it to extract computational content from proofs about abstract structures specified by arbitrary classically true disjunction free formulas. The interpretation is shown to be

    更新日期:2020-10-16
  • Unbounded towers and products
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-10-08
    Piotr Szewczak; Magdalena Włudecka

    We investigate products of sets of reals with combinatorial covering properties. A topological space satisfies S1(Γ,Γ) if for each sequence of point-cofinite open covers of the space, one can pick one element from each cover and obtain a point-cofinite cover of the space. We prove that, if there is an unbounded tower, then there is a nontrivial set of reals satisfying S1(Γ,Γ) in all finite powers.

    更新日期:2020-10-13
  • A microscopic approach to Souslin-tree construction, Part II
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-10-13
    Ari Meir Brodsky; Assaf Rinot

    In Part I of this series, we presented the microscopic approach to Souslin-tree constructions, and argued that all known ⋄-based constructions of Souslin trees with various additional properties may be rendered as applications of our approach. In this paper, we show that constructions following the same approach may be carried out even in the absence of ⋄. In particular, we obtain a new weak sufficient

    更新日期:2020-10-13
  • Indestructibility of ideals and MAD families
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-10-13
    David Chodounský; Osvaldo Guzmán

    In this survey paper we collect several known results on destroying tall ideals on countable sets and maximal almost disjoint families with forcing. In most cases we provide streamlined proofs of the presented results. The paper contains results of many authors as well as a preview of results of a forthcoming paper of Brendle, Guzmán, Hrušák, and Raghavan.

    更新日期:2020-10-13
  • Corson reflections
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-10-13
    Ilijas Farah; Menachem Magidor

    A reflection principle for Corson compacta holds in the forcing extension obtained by Levy-collapsing a supercompact cardinal to ℵ2. In this model, a compact Hausdorff space is Corson if and only if all of its continuous images of weight ℵ1 are Corson compact. We use the Gelfand–Naimark duality, and our results are stated in terms of unital abelian C⁎-algebras.

    更新日期:2020-10-13
  • An Efimov space with character less than s
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-10-13
    Alan Dow

    It is consistent that there is a compact space of character less than the splitting number in which there are no converging sequences. Such a space is an Efimov space.

    更新日期:2020-10-13
  • Definable MAD families and forcing axioms
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-10-13
    Vera Fischer; David Schrittesser; Thilo Weinert

    We show that ZFC + BPFA (i.e., the Bounded Proper Forcing Axiom) + “there are no Π21 infinite MAD families” implies that ω1 is a remarkable cardinal in L. In other words, under BPFA and an anti-large cardinal assumption there is a Π21 infinite MAD family. It follows that the consistency strength of ZFC + BPFA + “there are no projective infinite MAD families” is exactly a Σ1-reflecting cardinal above

    更新日期:2020-10-13
  • The Borel complexity of von Neumann equivalence
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-10-13
    Inessa Moroz; Asger Törnquist

    We prove that for a countable discrete group Γ containing a copy of the free group Fn, for some 2≤n≤∞, as a normal subgroup, the equivalence relations of conjugacy, orbit equivalence and von Neumann equivalence of the ergodic a.e. free probability measure preserving actions of Γ are analytic non-Borel equivalence relations in the Polish space of probability measure preserving Γ-actions. As a consequence

    更新日期:2020-10-13
  • Two Applications of Topology to Model Theory
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-10-13
    Christopher J. Eagle; Clovis Hamel; Franklin D. Tall

    By utilizing the topological concept of pseudocompactness, we simplify and improve a proof of Caicedo, Dueñez, and Iovino concerning Terence Tao's metastability. We also pinpoint the exact relationship between the Omitting Types Theorem and the Baire Category Theorem by developing a machine that turns topological spaces into abstract logics.

    更新日期:2020-10-13
  • Separating families and order dimension of Turing degrees
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-10-13
    Ashutosh Kumar; Dilip Raghavan

    We study families of functions and linear orders which separate countable subsets of the continuum from points. As an application, we show that the order dimension of the Turing degrees, denoted dimT, cannot be decided in ZFC. We also provide a combinatorial description of dimT and show that the Turing degrees have the largest order dimension among all locally countable partial orders of size continuum

    更新日期:2020-10-13
  • Some remarks on the Open Coloring Axiom
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-10-12
    Justin Tatch Moore

    This note contains two results relating to the problem of whether the Open Coloring Axiom implies that the continuum is ℵ2. It also establishes that Farah's OCA∞ is equivalent to OCA.

    更新日期:2020-10-12
  • Convergent sequences in topological groups
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-10-12
    Michael Hrušák; Alexander Shibakov

    We survey recent developments concerning the role of convergent sequences in topological groups. We present the Invariant Ideal Axiom and announce its effect on convergence properties in topological groups, in particular, the consistency of the fact that every countable sequential topological group is either metrizable or kω. We also outline a construction of a countably compact topological group without

    更新日期:2020-10-12
  • The canonical pairs of bounded depth Frege systems
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-10-02
    Pavel Pudlák

    The canonical pair of a proof system P is the pair of disjoint NP sets where one set is the set of all satisfiable CNF formulas and the other is the set of CNF formulas that have P-proofs bounded by some polynomial. We give a combinatorial characterization of the canonical pairs of depth d Frege systems. Our characterization is based on certain games, introduced in this article, that are parametrized

    更新日期:2020-10-06
  • Computable Irrational Numbers with Representations of Surprising Complexity
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-10-06
    Ivan Georgiev; Lars Kristiansen; Frank Stephan

    Cauchy sequences, Dedekind cuts, base-10 expansions and continued fractions are examples of well-known representations of irrational numbers. But there exist others, not so popular, which can be defined using various kinds of sum approximations and best approximations. In this paper we investigate the complexity of a number of such representations. For any fast-growing computable function f, we define

    更新日期:2020-10-06
  • Stationary and closed rainbow subsets
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-09-23
    Shimon Garti; Jing Zhang

    We study the structural rainbow Ramsey theory at uncountable cardinals. Compared to the usual rainbow Ramsey theory, the variation focuses on finding a rainbow subset that not only is of a certain cardinality but also satisfies certain structural constraints, such as being stationary or closed in its supremum. In the process of dealing with cardinals greater than ω1, we uncover some connections between

    更新日期:2020-09-28
  • Small models, large cardinals, and induced ideals
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-09-23
    Peter Holy; Philipp Lücke

    We show that many large cardinal notions up to measurability can be characterized through the existence of certain filters for small models of set theory. This correspondence will allow us to obtain a canonical way in which to assign ideals to many large cardinal notions. This assignment coincides with classical large cardinal ideals whenever such ideals had been defined before. Moreover, in many important

    更新日期:2020-09-28
  • On the number of independent orders
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-09-15
    Kota Takeuchi; Akito Tsuboi

    We investigate the model-theoretic invariant κsrdm(T), which was introduced by Shelah, and prove that κsrdm(T) is sub-additive. An infinite value of κsrdm(T) leads to the equality κsrdm(T)=κsrd1(T). We apply the same proof method to analyze the other invariant κirdm(T) and show that it is also sub-additive, achieving an improvement of Shelah's result.

    更新日期:2020-09-26
  • First-order model theory of free projective planes
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-09-22
    Tapani Hyttinen; Gianluca Paolini

    We prove that the theory of open projective planes is complete and strictly stable, and infer from this that Marshall Hall's free projective planes (πn:4⩽n⩽ω) are all elementary equivalent and that their common theory is strictly stable and decidable, being in fact the theory of open projective planes. We further characterize the elementary substructure relation in the class of open projective planes

    更新日期:2020-09-25
  • Derivatives of normal functions in reverse mathematics
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-09-24
    Anton Freund; Michael Rathjen

    Consider a normal function f on the ordinals (i. e. a function f that is strictly increasing and continuous at limit stages). By enumerating the fixed points of f we obtain a faster normal function f′, called the derivative of f. The present paper investigates this important construction from the viewpoint of reverse mathematics. Within this framework we must restrict our attention to normal functions

    更新日期:2020-09-24
  • Algebraic combinatorics in bounded induction
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-09-03
    Joaquín Borrego-Díaz

    In this paper, new methods for analyzing models of weak subsystems of Peano Arithmetic are proposed. The focus will be on the study of algebro-combinatoric properties of certain definable cuts. Their relationship with segments that satisfy more induction, with those limited by the standard powers/roots of an element, and also with definable sets in Bounded Induction is studied. As a consequence, some

    更新日期:2020-09-03
  • Tukey order, calibres and the rationals
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-08-17
    Paul Gartside, Ana Mamatelashvili

    One partially ordered set, Q, is a Tukey quotient of another, P – denoted P≥TQ – if there is a map ϕ:P→Q carrying cofinal sets of P to cofinal sets of Q. Let X be a space and denote by K(X) the set of compact subsets of X, ordered by inclusion. For certain separable metrizable spaces M, Tukey upper and lower bounds of K(M) are calculated. Results on invariants of K(M)'s are deduced. The structure of

    更新日期:2020-08-17
  • When Pκ(λ) (vaguely) resembles κ
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-08-14
    Pierre Matet

    Let μ<κ<λ be three infinite cardinals, the first two being regular. Assuming the existence of a cofinal subset of (Pκ(λ),⊆) of size λ, we define an ideal on Pκ(λ) which we argue to be the analog for Pκ(λ) of NSκ|Eμκ (the restriction of the nonstationary ideal on κ to the set of limit ordinals less than κ of cofinality μ). We show that this ideal on Pκ(λ) is the ideal dual to the well-known μ-club filter

    更新日期:2020-08-14
  • Probabilistic Characterisation of Models of First-Order Theories
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-08-11
    Soroush Rafiee Rad

    We study probabilistic characterisation of a random model of a finite set of first order axioms. Given a set of first order axioms T and a structure M which we only know is a model of T, we are interested in the probability that M would satisfy a sentence ψ. Answering this question for all sentences in the language will give a probability distribution over the set of sentences which can be regarded

    更新日期:2020-08-11
  • Ax-Schanuel and strong minimality for the j-function
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-08-04
    Vahagn Aslanyan

    Let K:=(K;+,⋅,D,0,1) be a differentially closed field of characteristic 0 with field of constants C. In the first part of the paper we explore the connection between Ax-Schanuel type theorems (predimension inequalities) for a differential equation E(x,y) and the geometry of the fibres Us:={y:E(s,y)∧y∉C} where s is a non-constant element. We show that certain types of predimension inequalities imply

    更新日期:2020-08-04
  • Computable analogs of cardinal characteristics: Prediction and rearrangement
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-08-03
    Iván Ongay-Valverde, Paul Tveite

    There has recently been work by multiple groups in extracting the properties associated with cardinal invariants of the continuum and translating these properties into similar analogous combinatorial properties of computational oracles. Each property yields a highness notion in the Turing degrees. In this paper we study the highness notions that result from the translation of the evasion number and

    更新日期:2020-08-03
  • Towards the entropy-limit conjecture
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-07-24
    Jürgen Landes, Soroush Rafiee Rad, Jon Williamson

    The maximum entropy principle is widely used to determine non-committal probabilities on a finite domain, subject to a set of constraints, but its application to continuous domains is notoriously problematic. This paper concerns an intermediate case, where the domain is a first-order predicate language. Two strategies have been put forward for applying the maximum entropy principle on such a domain:

    更新日期:2020-07-24
  • Preservation theorems for Namba forcing
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-07-23
    Osvaldo Guzmán, Michael Hrušák, Jindřich Zapletal

    We study preservation properties of Namba forcing on κ. We prove that if I is an ideal with a Borel base on ωω and κ>ω1 is a regular cardinal less than the uniformity number or bigger than the covering number of I, then the κ-Namba forcing preserves the covering of I. The situation at κ=ω1, also treated here, is more complex.

    更新日期:2020-07-23
  • Complexity of syntactical tree fragments of Independence-Friendly logic
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-07-17
    Fausto Barbero

    A dichotomy result of Sevenster (2014) [29] completely classified the quantifier prefixes of regular Independence-Friendly (IF) logic according to the patterns of quantifier dependence they contain. On one hand, prefixes that contain “Henkin” or “signalling” patterns were shown to characterize fragments of IF logic that capture NP-complete problems; all the remaining prefixes were shown instead to

    更新日期:2020-07-17
  • Open core and small groups in dense pairs of topological structures
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-07-16
    Elías Baro, Amador Martin-Pizarro

    Dense pairs of geometric topological fields have tame open core, that is, every definable open subset in the pair is already definable in the reduct. We fix a minor gap in the published version of van den Dries's seminal work on dense pairs of o-minimal groups, and show that every definable unary function in a dense pair of geometric topological fields agrees with a definable function in the reduct

    更新日期:2020-07-16
  • Finitely generated groups are universal among finitely generated structures
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-07-03
    Matthew Harrison-Trainor, Meng-Che “Turbo” Ho

    Universality has been an important concept in computable structure theory. A class C of structures is universal if, informally, for any structure of any kind there is a structure in C with the same computability-theoretic properties as the given structure. Many classes such as graphs, groups, and fields are known to be universal. This paper is about the class of finitely generated groups. Because finitely

    更新日期:2020-07-03
  • |˜-divisibility of ultrafilters
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-07-03
    Boris Šobot

    We further investigate a divisibility relation on the set βN of ultrafilters on the set of natural numbers. We single out prime ultrafilters (divisible only by 1 and themselves) and establish a hierarchy in which a position of every ultrafilter depends on the set of prime ultrafilters it is divisible by. We also construct ultrafilters with many immediate successors in this hierarchy and find positions

    更新日期:2020-07-03
  • Filter-linkedness and its effect on preservation of cardinal characteristics
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-06-29
    Jörg Brendle, Miguel A. Cardona, Diego A. Mejía

    We introduce the property “F-linked” of subsets of posets for a given free filter F on the natural numbers, and define the properties “μ-F-linked” and “θ-F-Knaster” for posets in a natural way. We show that θ-F-Knaster posets preserve strong types of unbounded families and of maximal almost disjoint families. Concerning iterations of such posets, we develop a general technique to construct θ-Fr-Knaster

    更新日期:2020-06-29
  • On equivalence relations generated by Cauchy sequences in countable metric spaces
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-06-25
    Longyun Ding, Kai Gu

    Let X be the set of all metrics on ω, and let Xcpt be the set of all metrics r on ω such that the completion of (ω,r) is compact. We define the Cauchy sequence equivalence relation Ecs on X as: rEcss iff the set of Cauchy sequences in (ω,r) is same as in (ω,s). We also denote Ecsc=Ecs↾Xcpt. We show that Ecs is a Π11-complete equivalence relation, while Ecsc is a Π30 equivalence relation. We also show

    更新日期:2020-06-25
  • The tree property at double successors of singular cardinals of uncountable cofinality with infinite gaps
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-06-18
    Mohammad Golshani; Alejandro Poveda

    Assume that κ and λ are respectively strong and weakly compact cardinals with λ>κ. Fix Θ≥λ a cardinal with cof(Θ)>κ and cof(δ)=δ<κ. Assuming the GCH≥κ holds, we construct a generic extension of the universe where κ is a strong limit cardinal, cof(κ)=δ, 2κ=Θ and TP(κ++) holds. This extends the main result of [4] for uncountable cofinalities.

    更新日期:2020-06-18
  • Proofs and surfaces
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-06-01
    Djordje Baralić, Pierre-Louis Curien, Marina Milićević, Jovana Obradović, Zoran Petrić, Mladen Zekić, Rade T. Živaljević

    A formal sequent system dealing with Menelaus' configurations is introduced in this paper. The axiomatic sequents of the system stem from 2-cycles of Δ-complexes. The Euclidean and projective interpretations of the sequents are defined and a soundness result is proved. This system is decidable and its provable sequents deliver incidence results. A cyclic operad structure tied to this system is presented

    更新日期:2020-06-01
  • Structure and representation of semimodules over inclines
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-05-29
    Ruiqi Bai, Yichuan Yang

    An incline S is a commutative semiring where r+1=1 for any r∈S. We note that the ideal lattice of an S-semimodule is naturally an S-semimodule and so is its congruence lattice when S is transitive. We prove that the categories of complete S-semimodules, together with dual functor, internal hom and tensor product, is a ⋆-autonomous category. We define the locally and globally maximal congruences which

    更新日期:2020-05-29
  • The FAN principle and weak König's lemma in herbrandized second-order arithmetic
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-05-28
    Fernando Ferreira

    We introduce a herbrandized functional interpretation of a first-order semi-intuitionistic extension of Heyting Arithmetic and study its main properties. We then extend the interpretation to a certain system of second-order arithmetic which includes a (classically false) formulation of the FAN principle and weak König's lemma. It is shown that any first-order formula provable in this system is classically

    更新日期:2020-05-28
  • Join-completions of partially ordered algebras
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-05-23
    José Gil-Férez, Luca Spada, Constantine Tsinakis, Hongjun Zhou

    We present a systematic study of join-extensions and join-completions of partially ordered algebras, which naturally leads to a refined and simplified treatment of fundamental results and constructions in the theory of ordered structures ranging from properties of the Dedekind–MacNeille completion to the proof of the finite embeddability property for a number of varieties of lattice-ordered algebras

    更新日期:2020-05-23
  • Ultrafilters, finite coproducts and locally connected classifying toposes
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-05-19
    Richard Garner

    We prove a single category-theoretic result encapsulating the notions of ultrafilters, ultrapower, ultraproduct, tensor product of ultrafilters, the Rudin–Kiesler partial ordering on ultrafilters, and Blass's category of ultrafilters UF. The result in its most basic form states that the category FC(Set,Set) of finite-coproduct-preserving endofunctors of Set is equivalent to the presheaf category [UF

    更新日期:2020-05-19
  • Polish metric spaces with fixed distance set
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-05-19
    Riccardo Camerlo, Alberto Marcone, Luca Motto Ros

    We study Polish spaces for which a set of possible distances A⊆R+ is fixed in advance. We determine, depending on the properties of A, the complexity of the collection of all Polish metric spaces with distances in A, obtaining also example of sets in some Wadge classes where not many natural examples are known. Moreover we describe the properties that A must have in order that all Polish spaces with

    更新日期:2020-05-19
  • Diagonal supercompact Radin forcing
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-05-18
    Omer Ben-Neria, Chris Lambie-Hanson, Spencer Unger

    Motivated by the goal of constructing a model in which there are no κ-Aronszajn trees for any regular κ>ℵ1, we produce a model with many singular cardinals where both the singular cardinals hypothesis and weak square fail.

    更新日期:2020-05-18
  • Rules with parameters in modal logic II
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-05-15
    Emil Jeřábek

    We analyze the computational complexity of admissibility and unifiability with parameters in transitive modal logics. The class of cluster-extensible (clx) logics was introduced in the first part of this series of papers [8]. We completely classify the complexity of unifiability or inadmissibility in any clx logic as being complete for one of Σ2exp, NEXP, coNEXP, PSPACE, or Π2p. In addition to the

    更新日期:2020-05-15
  • Modal extension of ideal paraconsistent four-valued logic and its subsystem
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-05-15
    Norihiro Kamide, Yoni Zohar

    This study aims to introduce a modal extension M4CC of Arieli, Avron, and Zamansky's ideal paraconsistent four-valued logic 4CC as a Gentzen-type sequent calculus and prove the Kripke-completeness and cut-elimination theorems for M4CC. The logic M4CC is also shown to be decidable and embeddable into the normal modal logic S4. Furthermore, a subsystem of M4CC, which has some characteristic properties

    更新日期:2020-05-15
Contents have been reproduced by permission of the publishers.
导出
全部期刊列表>>
微生物研究
亚洲大洋洲地球科学
NPJ欢迎投稿
自然科研论文编辑
ERIS期刊投稿
欢迎阅读创刊号
自然职场,为您触达千万科研人才
spring&清华大学出版社
城市可持续发展前沿研究专辑
Springer 纳米技术权威期刊征稿
全球视野覆盖
施普林格·自然新
chemistry
物理学研究前沿热点精选期刊推荐
自然职位线上招聘会
欢迎报名注册2020量子在线大会
化学领域亟待解决的问题
材料学研究精选新
GIANT
ACS ES&T Engineering
ACS ES&T Water
屿渡论文,编辑服务
阿拉丁试剂right
上海中医药大学
清华大学
复旦大学
南科大
北京理工大学
上海交通大学
隐藏1h前已浏览文章
课题组网站
新版X-MOL期刊搜索和高级搜索功能介绍
ACS材料视界
王鹏
武汉大学
浙江大学
天合科研
x-mol收录
试剂库存
down
wechat
bug